Statistics related question : Mean = Median

[JbhB682]

Hi

Is the mean = median at all times for the following two cases only ?

case 1) all numbers within a set are the same

case 2) ALL evenly spaced set (the difference between the numbers can be 4 or 10 or 20) -- in evenly spaced sets ..the mean ALWAYS equals the median


i have tried doing some test cases and i believe these are the ONLY two scenario's where the mean MUST EQUAL the median

Please let me know your thoughts

[Sage Pearce-Higgins]

Yes, for evenly spaced sets, the mean is equal to the median. (If all the numbers in a set are the same, then that set is evenly spaced, as the space between the items is 0.) That's a useful thing to know, particularly when it comes to calculating the sum of a set.

However, you could construct a non-evenly spaced set in which the mean is equal to the median as well, such as {1, 1, 3, 3, 7}.

[JbhB682]

thank you

[Sage Pearce-Higgins]

You're welcome.

[JbhB682]

Hi - Sage :

just wondering -- is it possible for an un-evenly spaced set with an even number of integers in the set

can the mean EVER equal the median ?

i have tried testing a few cases but i could not find one

[Sage Pearce-Higgins]

Good exercise, let's try to make a set that has that property. Pick a number to be both mean and median: let's say 4. Since we want an even number of terms, then we can make the two middle numbers in the set 3 and 5. Now, let's make the set bigger. To keep the median the same, we'd need to add one number higher than 5 and one number lower than 3. Currently the gap between the numbers is 2, so if we want a non-evenly spaced set, we'd need to try to include a different gap. How about including the numbers 2 and 6. This would make our set {2, 3, 5, 6}. That works. Can you find another set that has that property?

[JbhB682]

I think even the following property works for non-evenly spaced set

-- a sequence but the middle number is missing

example :

1) [ 0 / 2 / 6 / 8 ]

2) [10, 11, 13, 14]

3) [10, 20, 40, 50]

[Sage Pearce-Higgins]

No need to repost my previous post in your reply.

Yes, absolutely, missing out the middle number of an evenly spaced set with an odd number of terms gives a set with the property that mean = median, but that is not evenly-spaced. Nice work.